In how many ways can 8 people be seated in a row if there are 4 men and 4 women and no 2 men or 2 women can sit next to each other?

There are 1152 ways to seat 8 people such that no two men or women are sitting together.

Step-by-step explanation:

In a group of 8 people there are 4 men and 4 women.

These 8 people are to seated in a row such that no 2 men or 2 women can sit next to each other.

That is, men and women are sitting alternatively.

M, W, M, W, M, W, M, W

This can happen in 2 ways because the first place can be occupied by a women.

Compute the number of ways of seating 8 people as follows:

The 4 men can sit in 4! ways.

The 4 women can sit in 4! ways.

The number of ways is: 4! × 4! × 2 =  1152

Thus, there are 1152 ways to seat 8 people such that no two men or women are sitting together.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

12r - 8 - 12

you have to combine like terms. below i have bolded the like terms:

12r - 8 - 12

together it combines to:

12r - 20

hope this !